Question: (10 pts.) Suppose that F(x,y) is a continuous function defined on R=[0,1][0,1] such that the partial derivative delRF exists and is continuous on (0,1)[0,1]. Let

(10 pts.) Suppose that F(x,y) is a continuous function defined on R=[0,1][0,1] such that the partial derivative delRF exists and is continuous on (0,1)[0,1]. Let us define f:[0,1]R asf(x)=01F(x,y)dy,;xin[0,1]Prove that f is differentiable on (0,1) and satisfiesf'(x)=01xF(x,y)dy,;xin(0,1)

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